The generator matrix

 1  0  0  0  1  1  1 3X+2  1 3X+2  1  X  1 2X+2  1  1  1  1  1 3X  2  1 2X  1 3X+2  0  1 2X+2  2  1 X+2  1  X  1  1  1  1  1  1 3X+2  0  1  1  X  0  0  1 3X  1  X  1 2X+2 3X+2 3X  1  1  1 X+2 2X 3X  1  1  1  1 3X+2 3X  1  1  0 2X 3X  1  1 X+2 3X  1  1 X+2  1  1 2X+2  1  1
 0  1  0  0 2X  3 3X+1  1 2X+2 2X+2 2X+2  1 3X+3  1 2X+3  1  0 3X+2 X+2 3X  1 X+3  1  2 2X  1 X+3  1 2X  3 3X 3X+3  1  0 3X+2 2X+1  X X+1 2X  1  1  2 X+1  1 2X  1 3X  1 X+1 X+2 X+2 3X  1  1 3X  X 2X+3  1  2  2 3X 3X+2  1  2  1  1 2X+3 3X+3  1  1  1  2 X+2 2X  1 3X  X  1  2 3X+1  1 X+1 2X
 0  0  1  0  2 2X 2X+2 2X+2  1  1 X+3 X+3  3 X+1 3X+3 2X+3 2X+1 2X 2X+1  1 X+2 X+2 3X+1 3X+2  1  X 2X+2 2X+3  1  1 2X 2X+3  X  2  3 3X+2  3 X+2  X 2X+3 3X+3 3X X+1 3X+1 3X+2 3X  X 3X+3  0  1  1  1 2X X+1 X+1 X+2  0  X  1  1 3X 3X+3 3X 3X  2 2X+3 2X+3  1 2X+2 3X  2 2X+1 X+1  1 2X 3X+1 3X  3 3X+1 X+1 2X+1 3X+1 2X+2
 0  0  0  1 3X+3 X+3 2X X+1 3X+1 X+3  0 2X+1 3X+2 3X  3 3X+1 3X 2X+3 3X+3 2X+2  1 X+1 3X+1  2  1  2  X 3X+2 3X+1 2X+1  1  0 2X X+2 2X+2  0  1 2X+1 3X X+3 2X+2  3 X+2  2  1 3X 2X+3 X+3 X+1  X X+2 X+1 2X+1 3X 3X+3 X+2 2X  1 2X+1 2X+2 3X+1 2X 3X+3 X+1  3 2X+1 3X 2X+3 2X+1 2X+3 3X+3  0  X X+2 2X+2 2X+3  0  2 3X+1 2X+2  0  X 2X

generates a code of length 83 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+518x^76+1728x^77+2877x^78+4636x^79+5768x^80+6322x^81+7908x^82+7392x^83+7381x^84+6172x^85+5345x^86+4060x^87+2499x^88+1438x^89+784x^90+392x^91+165x^92+96x^93+13x^94+16x^95+20x^96+4x^97+1x^102

The gray image is a code over GF(2) with n=664, k=16 and d=304.
This code was found by Heurico 1.16 in 49.9 seconds.